Logical Reasoning previous years questions (CAT) - Set 0010


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    Previous years`s CAT questions: Logical Reasoning

    Post your solutions as reply to respective questions below.


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    Question 1

    A significant amount of traffic flows from point S to point T in the one-way street network shown below. Points A, B, C, and D are junctions in the network, and the arrows mark the direction of traffic flow. The fuel cost in rupees for travelling along a street is indicated by the number adjacent to the arrow representing the street.

    Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling is the minimum. If two or more routes have the same least travel cost, then motorists are indifferent between them. Hence, the traffic gets evenly distributed among all the least cost routes. The government can control the flow of traffic only by levying appropriate toll at each junction. For example, if a motorist takes the route S-A-T (using junction A alone), then the total cost of travel would be Rs 14 (i.e. Rs 9 + Rs 5) plus the toll charged at junction A.

    1) If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

    (1) 2, 5, 3, 2
    (2) 0, 5, 3, 1

    (3) 1, 5, 3, 2
    (4) 2, 3, 5, 1
    (5) 1, 3, 5, 1             

    2) If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

    (1) 1, 5, 3, 3
    (2) 1, 4, 4, 3
    (3) 1, 5, 4, 2
    (4) 0, 5, 2, 3
    (5) 0, 5, 2, 2             

    3) If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

    (1) 0, 5, 2, 2
    (2) 0, 5, 4, 1
    (3) 1, 5, 3, 3
    (4) 1, 5, 3, 2
    (5) 1, 5, 4, 2             

    4) If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

    (1) 0, 5, 4, 1
    (2) 0, 5, 2, 2

    (3) 1, 5, 3, 3
    (4) 1, 5, 3, 2
    (5) 0, 4, 3, 2             

    5) The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:

    (1) Rs 7
    (2) Rs 9
    (3) Rs 10
    (4) Rs 13
    (5) Rs 14          (CAT 2006)


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    Question 2

    K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

    A team must include exactly one among P, R, and S.

    A team must include either M or Q, but not both.

    If a team includes K, then it must also include L, and vice versa.

    If a team includes one among S, U, and W, then it must also include the other two.

    L and N cannot be members of the same team.

    L and U cannot be members of the same team.

    The size of a team is defined as the number of members in the team. 

    1) What could be the size of a team that includes K?

    (1) 2 or 3
    (2) 2 or 4
    (3) 3 or 4
    (4) Only 2
    (5) Only 4                

    2) In how many ways a team can be constituted so that the team includes N?

    (1) 2          (2) 3         (3) 4                (4)5          (5) 6           

    3) What would be the size of the largest possible team?

    (1) 8         (2) 7          (3) 6                 (4) 5         (5) Cannot be determined    

    4) Who can be a member of a team of size 5?

    (1) K         (2) L           (3) M               (4) P         (5) R                

    5) Who cannot be a member of a team of size 3?

    (1) L         (2) M           (3) N               (4) P          (5) Q          (CAT 2006)   


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    Question 3

    In a Class X Board examination, ten papers are distributed over five Groups i.e. PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below. (Dipan’s score in English Paper II has been intentionally removed in the table) 

    Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl.

    1) How much did Dipan get in English Paper II?

    (1) 94              (2) 96.5            (3) 97              (4) 98              (5) 99             

    2) Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize. Among those who are eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to:

    (1) Shreya    (2) Ram      (3) Ayesha      (4) Dipan      (5) no one from the top ten         

    3) Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups?

    (1) 1                (2) 2                 (3) 3                 (4) 4        (5) 5                

    4) Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was:

    (1) Ram     (2) Agni      (3) Pritam     (4) Ayesha      (5) Dipan         

    5) Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group, then their standing in decreasing order of final score would be:

    (1) Pritam, Joseph, Tirna, Agni
    (2) Joseph, Tirna, Agni, Pritam
    (3) Pritam, Agni, Tirna, Joseph
    (4) Joseph, Tirna, Pritam, Agni
    (5) Pritam, Tirna, Agni, Joseph             (CAT 2006)


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    Question 4

    Answer the following questions based on the statements given below:

    There are three houses on each side of the road.
    These six houses are labeled as P, Q, R, S, T and U.

    The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White.
    The houses are of different heights.
    T, the tallest house, is exactly opposite to the Red coloured house.
    The shortest house is exactly opposite to the Green coloured house.
    U, the Orange coloured house, is located between P and S.
    R, the Yellow coloured house, is exactly opposite to P.
    Q, the Green coloured house, is exactly opposite to U.

    P, the White coloured house, is taller than R, but shorter than S and Q.  

    1) What is the colour of the tallest house?

    (1) Red    (2) Blue    (3) Green    (4) Yellow     (5) none of these    

    2) What is the colour of the house diagonally opposite to the Yellow coloured house?

    (1) White    (2) Blue    (3) Green    (4) Red     (5) none of these   

    3) Which is the second tallest house?

    (1) P    (2) S     (3) Q    (4) R      (5) cannot be determined       (CAT 2008 )


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    Question 5

    In a sports event, six teams (A, B, C, D, E and F) are competing against each other. Matches are scheduled in two stages. Each team plays three matches in Stage-I and two matches in Stage-II. No team plays against the same team more than once in the event. No ties are permitted in any of the matches. The observations after the completion of Stage-I and Stage-II are as given below.

    Stage - I:

    • One team won all the three matches.
    • Two teams lost all the matches.
    • D lost to A but won against C and F.
    • E lost to B but won against C and F.
    • B lost at least one match.
    • F did not play against the top team of Stage- I.

    Stage - II:

    • The leader of Stage-I lost the next two matches.
    • Of the two teams at the bottom after Stage-I, one team won both matches, while the other lost both matches.
    • One more team lost both matches in Stage- II.      

    1) The team(s) with the most wins in the event is (are):

    (1) A     (2) A & C     (3) F     (4) E      (5) B & E  

    2) The two teams that defeated the leader of Stage-I are:

    (1) F & D     (2) E & F     (3) B & D      (4) E & D      (5) F & D

    3) The only team(s) that won both the matches in Stage-II is (are):

    (1) B      (2) E & F       (3) A, E & F      (4) B, E & F     (5) B & F  

    4) The teams that won exactly two matches in the event are:

    (1) A, D & F    (2) D & E      (3) E & F     (4) D, E & F     (5) D & F 

    (CAT 2008 )


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